6 ideas
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
| From: Paul Bernays (On Platonism in Mathematics [1934]) |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
| A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
| A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
| 16643 | Accidents always remain suited to a subject [Bonaventura] |
| Full Idea: An accident's aptitudinal relationship to a subject is essential, and this is never taken away from accidents….for it is true to say that they are suited to a subject. | |
| From: Bonaventura (Commentary on Sentences [1252], IV.12.1.1.1c) | |
| A reaction: This is the compromise view that allows accidents to be separated, for Transubstantiation, while acknowledging that we identify them with their subjects. |
| 16696 | Successive things reduce to permanent things [Bonaventura] |
| Full Idea: Everything successive reduces to something permanent. | |
| From: Bonaventura (Commentary on Sentences [1252], II.2.1.1.3 ad 5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.2 | |
| A reaction: Avicenna first took successive entities seriously, but Bonaventure and Aquinas seem to have rejected them, or given reductive accounts of them. It resembles modern actualists versus modal realists. |
| 16618 | Intellectual and moral states, and even the soul itself, depend on prime matter for their existence [Blasius, by Pasnau] |
| Full Idea: Blasius argued that prime matter is the subject of all our intellectual and moral states. This implies that such states cannot exist apart from the body, which seems to imply further that the soul itself cannot exist apart from the body. | |
| From: report of Blasius of Parma (Les quaestiones de anima (lectures on the soul) [1385], I.8 p.65) by Robert Pasnau - Metaphysical Themes 1274-1671 06.3 | |
| A reaction: It seems that, under pressure, Blasius recanted this view in lectures given eleven years later. |